Robust Bayesian approach to logistic regression modeling in small sample size utilizing a weakly informative student’s t prior distribution

Abstract

This work discourages using the logistic regression (LR) model for estimative purposes when the sample size is small. We propose a new model called the “Robust Bayesian Logistic (RBL) model” that minimizes bias in the estimated logistic regression coefficients when the sample size is small, and covariate corruption is suspected. For the prior specification in the proposed RBL model, all the logistic regression coefficients are assigned independent Student’s t-distribution with the location parameter 0, scale parameter 1, and degree of freedom 7 for the constant term and degree of freedom of 1 for all other regression coefficients. In our experimental study, the proposed RBL model outperforms the Logistic Regression (LR) model by having a lower mean squared error (MSE) in the regression coefficients estimated for all the sample sizes considered. The proposed RBL model has a lower standard deviation than the LR model for all the estimated regression coefficients on the real-life dataset. We suggest that the proposed RBL model be considered for logistic modeling since it generates stable, consistent, and reliable estimates, especially when the sample size is small. The proposed RBL model is a fully Bayesian method implemented in the R environment using the RJAGS package.